3D texture (UVW map to UV map?)
What you are describing is exactly one of the uses of texture baking. In this case you could use either cycles or the old blender internal.
The process would be:

Texture the object.
UV unwrap the object.
Bake the Perlin noise texture.

I'm using cycles, but the same principles apply to the BI (in the blender internal renderer you can pick what type of noise generator it uses, cycles only has perlin noise.)
Texturing
Texturing is very easy, because it is all procedural. My material is super basic, just the noise texture and a gamma node to boost the color:

Yes I'm using a teapot as my demo.


UV Unwrapping
In edit mode simply select everything and hit U &gt; Smart UV Project. Depending on your model and what else you are going to do with it you might need a better UV map. Sufficient to say, smart uv project does not always do the best job. Yet if all you are going to do with it is bake a map, then this will do.

Texture Baking
Before you can bake the texture you need to create an image blender will bake to. So in the UV Image Editor create a new image. &quot;New&quot; button in the header. Or if the new button is not showing, then click the &quot;+&quot; plus button in the image data block control, its still in the header.
Important Add an Image Texture node to the material for your object. Set the texture to the image you just created. The Image Texture node should not be connected to anything, but it must be active.

All set for baking.
In the Properties window go to the Render tab and scroll down to the Baking section. Here change the bake type to Emit (notice I'm using an emission shader in my material), and hit the large Bake button.

Presto you have a 3D procedural texture baked to a 2D image for further use anywhere.